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Update rules and semantic universals
Luca Incurvati1, Giorgio Sbardolini1
1ILLC and Philosophy, University of Amsterdam, Amsterdam, The Netherlands.
Linguistics and Philosophy
|March 28, 2023
Summary
Natural languages only lexicalize a few logical operators, like "and" and "or". This study explains these lexical gaps and the Monotonicity Universal using dynamic logic and update potentials.
Area of Science:
- Linguistics
- Formal Semantics
- Logic
Background:
- Natural languages exhibit lexical gaps, omitting many logically possible operators.
- Lexicalized logical operators (connectives, quantifiers) adhere to the Monotonicity Universal (upward or downward monotonicity).
Purpose of the Study:
- To provide a logical explanation for lexical gaps in natural language.
- To explain the Monotonicity Universal based on the dynamic behavior of logical operators.
Main Methods:
- Defining 'update potentials' for logical operators as procedures to modify conversational context.
- Analyzing how updates depend on an operator's logical form and the speech act (assertion/rejection).
Main Results:
- The study proposes that the adequacy of update potentials limits which logical operators become lexicalized.
- The Monotonicity Universal is shown to follow logically from the properties of these operator updates.
Conclusions:
- Update potentials offer a framework for understanding the constraints on lexicalizing logical operators.
- The dynamic behavior of operators, specifically their update potentials, explains observed patterns in natural language.
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